Top-level namespace for Stokhos classes and functions. More...

Namespaces
	KL
	Namespace for analytic KL expansions.

Classes
class	AbstractPreconditionerFactory
	An abstract class to represent a generic preconditioner factory. More...

class	AdaptivityManager

class	ApproxGaussSeidelPreconditioner
	A stochastic preconditioner based on applying one iteration of approximate Gauss-Seidel. More...

class	ApproxJacobiPreconditioner
	A stochastic preconditioner based on applying two iterations of approximate Jacobi. More...

class	ApproxSchurComplementPreconditioner
	A stochastic preconditioner based on applying the approximate Schur complement preconditioner as defined by Sousedik, Ghanem, and Phipps, Numerical Linear Algebra and Applications, 2012. More...

class	BasisInteractionGraph

class	BlockDiagonalOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...

class	DiagEpetraOp
	An Epetra operator representing the block stochastic Galerkin operator. More...

class	EpetraMultiVectorOperator
	An adaptor that supplies the operator interface to a multi-vector. More...

class	EpetraMultiVectorOperatorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...

class	EpetraMultiVectorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...

class	EpetraOperatorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...

class	EpetraSparse3Tensor

class	EpetraVectorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...

class	FullyAssembledOperator
	An Epetra operator representing the block stochastic Galerkin operator generated by fully assembling the matrix. More...

class	FullyAssembledPreconditioner
	A stochastic preconditioner based on applying a preconditioner to the fully assembled operator. More...

class	IfpackPreconditionerFactory
	A factory for building Ifpack preconditioners. More...

class	InterlacedOperator
	An Epetra operator representing the block stochastic Galerkin operator generated by fully assembling the matrix. The ordering of this operator is interlaced. That means that all stochastic degrees of freedom associated with a deterministic degree of freedom are interlaced. The result is a large sparse matrix that is composed of small (relatively) dense blocks. More...

class	KLMatrixFreeOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...

class	KLReducedMatrixFreeOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...

class	KroneckerProductPreconditioner
	An Epetra operator representing applying the mean in a block stochastic Galerkin expansion. More...

class	MatrixFreeOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...

class	MeanBasedPreconditioner
	A stochastic preconditioner based on applying the inverse of the mean. More...

class	MLPreconditionerFactory
	A factory for building ML preconditioners. More...

class	MPBlockDiagonalPreconditioner
	A multi-point preconditioner based on applying the inverse of the diagonal. More...

class	MPInverseModelEvaluator
	Nonlinear, inverse multi-point ModelEvaluator. More...

class	MPMeanBasedPreconditioner
	A multi-point preconditioner based on applying the inverse of the mean. More...

class	MPModelEvaluator
	Multi-point model evaluator. More...

class	MPModelEvaluatorAdapter
	ModelEvaluator adapter that implements the multi-point evaluations through sampling. More...

class	MPPreconditioner
	An abstract class to represent a generic stochastic Galerkin preconditioner as an Epetra_Operator. More...

class	MPPreconditionerFactory
	Factory for generating stochastic Galerkin preconditioners. More...

class	ParallelData

class	PCECovarianceOp
	An Epetra operator representing the covariance operator of a polynomial chaos expansion. More...

class	PreconditionerFactory
	An class for building preconditioners. More...

class	ProductContainerTraits
	Base traits definition for ProductContainer. More...

class	ProductContainer
	A product (in the mathematical sense) container class whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...

class	ProductEpetraMultiVector
	A container class storing products of Epetra_MultiVector's. More...

class	ProductEpetraMultiVectorOperator
	A container class for products of Epetra_Vector's. More...

class	ProductEpetraOperator
	A container class for products of Epetra_Vector's. More...

class	ProductEpetraVector
	A container class for products of Epetra_Vector's. More...

class	ResponseStatisticModelEvaluator
	ModelEvaluator providing statistic response functions. More...

class	SGInverseModelEvaluator
	Nonlinear, inverse stochastic Galerkin ModelEvaluator. More...

class	SGModelEvaluator
	Nonlinear, stochastic Galerkin ModelEvaluator. More...

class	SGModelEvaluator_Adaptive
	Nonlinear, stochastic Galerkin ModelEvaluator that constructs an adapted Jacobian. More...

class	SGModelEvaluator_Interlaced
	Nonlinear, stochastic Galerkin ModelEvaluator that constructs a interlaced Jacobian. More...

class	SGModelEvaluatorBase
	Base class for stochastic Galerkin model evaluators. More...

class	SGOperator
	An abstract class to represent a generic stochastic Galerkin operator as an Epetra_Operator. More...

class	SGOperatorFactory
	Factory for generating stochastic Galerkin preconditioners. More...

class	SGPreconditioner
	An abstract class to represent a generic stochastic Galerkin preconditioner as an Epetra_Operator. More...

class	SGPreconditionerFactory
	Factory for generating stochastic Galerkin preconditioners. More...

class	SGQuadModelEvaluator
	ModelEvaluator adaptor that implements the stochastic Galerkin residual and Jacobian computations using quadrature. More...

class	SGQuadMPModelEvaluator
	ModelEvaluator adaptor that implements the stochastic Galerkin residual and Jacobian computations using quadrature. More...

class	VectorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...

class	EpetraVectorCloner
	Cloner for Epetra_Vector coefficients. More...

class	EpetraMultiVectorCloner
	Cloner for Epetra_MultiVector coefficients. More...

class	EpetraOperatorCloner
	Cloner for Epetra_Operator coefficients. More...

class	EpetraCrsMatrixCloner
	Cloner for Epetra_CrsMatrix coefficients. More...

class	ProductContainerTraits< Epetra_Vector >
	Specialization of ProductContainerTraits to Epetra_Vector coefficients. More...

class	ProductContainerTraits< Epetra_MultiVector >
	Specialization of ProductContainerTraits to Epetra_MultiVector coefficients. More...

class	ProductContainerTraits< Epetra_CrsMatrix >
	Specialization of ProductContainerTraits to Epetra_CrsMatrix coefficients. More...

class	ProductContainerTraits< Epetra_Operator >
	Specialization of ProductContainerTraits to Epetra_Operator coefficients. More...

class	HouseTriDiagPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...

class	MonoProjPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...

class	Multiply< BlockCrsMatrix< BlockSpec, MatrixValue, Kokkos::Cuda >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< CooProductTensor< TensorScalar, Kokkos::Cuda, Pack >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< CrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	DeviceProp

class	Multiply< BlockCrsMatrix< FlatSparse3Tensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< FlatSparse3Tensor_kji< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< LexicographicBlockSparse3Tensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< LinearSparse3Tensor< TensorScalar, Kokkos::Cuda, BlockSize >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< SimpleTiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< StochasticProductTensor< TensorScalar, TensorType, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	BlockMultiply< SymmetricDiagonalSpec< Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar , Kokkos::LayoutLeft, Kokkos::Cuda > >

class	Multiply< BlockCrsMatrix< StochasticProductTensor< ValueType, CrsProductTensor< ValueType, Kokkos::OpenMP >, Kokkos::OpenMP >, MatrixValue, Kokkos::OpenMP >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::OpenMP >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::OpenMP > >

class	Multiply< BlockCrsMatrix< StochasticProductTensor< ValueType, CrsProductTensor< ValueType, Kokkos::Serial >, Kokkos::Serial >, MatrixValue, Kokkos::Serial >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::Serial >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::Serial > >

class	BlockCrsMatrix
	CRS matrix of dense blocks. More...

class	Multiply< BlockCrsMatrix< BlockSpec, MatrixValue, Device >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Device >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Device > >

class	CooProductTensor
	Sparse product tensor using 'COO'-like storage format. More...

class	CooProductTensor< ValueType, ExecutionSpace, true >
	Specialization of CooProductTensor for packed (i,j,k) More...

class	CooProductTensor< ValueType, ExecutionSpace, false >
	Specialization of CooProductTensor for unpacked (i,j,k) More...

class	BlockMultiply< CooProductTensor< ValueType, Device, Pack > >

struct	DeviceConfig

class	CrsMatrix
	CRS matrix. More...

class	Multiply< CrsMatrix< MatrixValue, Device, Layout >, InputVectorType, OutputVectorType, void, IntegralRank< 1 > >

class	Multiply< CrsMatrix< MatrixValue, Device, Layout >, InputMultiVectorType, OutputMultiVectorType, std::vector< OrdinalType >, IntegralRank< 2 > >

class	Multiply< CrsMatrix< MatrixValue, Device, Layout >, InputMultiVectorType, OutputMultiVectorType, void, IntegralRank< 2 > >

class	Multiply< CrsMatrix< MatrixValue, Device, Layout >, std::vector< InputViewType >, std::vector< OutputViewType >, void, IntegralRank< 1 > >

class	SingleColumnMultivectorMultiply

class	MatrixMarketWriter< CrsMatrix< MatrixValue, Device, Layout > >

class	CrsProductTensor
	Sparse product tensor with replicated entries to provide subsets with a given coordinate. More...

class	BlockMultiply< CrsProductTensor< ValueType, Device > >

class	MultiplyImpl

class	FlatSparse3Tensor
	Sparse product tensor with replicated entries to provide subsets with a given coordinate. More...

class	BlockMultiply< FlatSparse3Tensor< ValueType, Device > >

class	FlatSparse3Tensor_kji
	Sparse product tensor with replicated entries to provide subsets with a given coordinate. More...

class	BlockMultiply< FlatSparse3Tensor_kji< ValueType, Device > >

class	LexicographicBlockSparse3Tensor
	Sparse product tensor with replicated entries to provide subsets with a given coordinate. More...

class	BlockMultiply< LexicographicBlockSparse3Tensor< ValueType, Device > >

class	LinearSparse3Tensor
	Sparse product tensor with replicated entries to provide subsets with a given coordinate. More...

class	BlockMultiply< LinearSparse3Tensor< ValueType, Device, BlockSize > >

class	MatrixMarketWriter

class	DefaultMultiply

class	IntegralRank

struct	ViewRank

struct	ViewRank< std::vector< T > >

class	Multiply

class	BlockMultiply

class	SimpleTiledCrsProductTensor

class	BlockMultiply< SimpleTiledCrsProductTensor< ValueType, Device > >

class	StochasticProductTensor
	Bases defined by combinatorial product of polynomial bases. More...

class	BlockMultiply< StochasticProductTensor< ValueType, TensorType, Device > >

class	SymmetricDiagonalSpec
	Symmetric diagonal storage for a dense matrix. More...

class	BlockMultiply< SymmetricDiagonalSpec< Device > >

class	TiledCrsProductTensor

class	BlockMultiply< TiledCrsProductTensor< ValueType, Device > >

class	TinyVec

class	TinyVec< ValueType, N, UseIntrinsics, true >

class	Update

class	Multiply< BlockCrsMatrix< StochasticProductTensor< ValueType, CrsProductTensor< ValueType, Kokkos::Threads >, Kokkos::Threads >, MatrixValue, Kokkos::Threads >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::Threads >, Kokkos::View< VectorValue , Kokkos::LayoutLeft, Kokkos::Threads > >

class	Multiply< KokkosSparse::CrsMatrix< Sacado::UQ::PCE< MatrixStorage >, MatrixOrdinal, MatrixDevice, MatrixMemory, MatrixSize >, Kokkos::View< Sacado::UQ::PCE< InputStorage > , InputP... >, Kokkos::View< Sacado::UQ::PCE< OutputStorage > , OutputP... > >

class	Multiply< KokkosSparse::CrsMatrix< Sacado::UQ::PCE< MatrixStorage >, MatrixOrdinal, MatrixDevice, MatrixMemory, MatrixSize >, Kokkos::View< Sacado::UQ::PCE< InputStorage > , InputP... >, Kokkos::View< Sacado::UQ::PCE< OutputStorage > , OutputP... > >

class	MeanMultiply

class	MeanMultiply< KokkosSparse::CrsMatrix< Sacado::UQ::PCE< MatrixStorage >, MatrixOrdinal, MatrixDevice, MatrixMemory, MatrixSize >, Kokkos::View< Sacado::UQ::PCE< InputStorage > , InputP... >, Kokkos::View< Sacado::UQ::PCE< OutputStorage > , OutputP... > >

class	MeanMultiply< KokkosSparse::CrsMatrix< Sacado::UQ::PCE< MatrixStorage >, MatrixOrdinal, MatrixDevice, MatrixMemory, MatrixSize >, Kokkos::View< Sacado::UQ::PCE< InputStorage > , InputP... >, Kokkos::View< Sacado::UQ::PCE< OutputStorage > , OutputP... > >

struct	DeviceForNode2

struct	DeviceForNode2< Kokkos::Compat::KokkosDeviceWrapperNode< Device > >

class	DynamicStorage

class	DynamicStridedStorage

class	DynamicThreadedStorage
	Dynamically allocated storage class with striding. More...

struct	IsScalarType2
	Base template specification for IsScalarType. More...

struct	IsScalarType2< float >

struct	IsScalarType2< double >

struct	IsScalarType2< int >

struct	IsScalarType2< long >

struct	DynArrayTraits
	Dynamic array allocation class that is specialized for scalar i.e., fundamental or built-in types (float, double, etc...). More...

struct	DynArrayTraits< T, device_t, false >
	Dynamic array allocation class that works for any type. More...

struct	MemoryTraits
	Traits class encapsulting memory alignment. More...

struct	MemoryTraits< Kokkos::HostSpace >
	Specialization of MemoryTraits for host memory spaces. More...

class	aligned_allocator
	An aligned STL allocator. More...

class	aligned_allocator< const T >
	An aligned STL allocator. More...

struct	StaticArrayTraits
	Static array allocation class. More...

struct	StaticArrayTraits< T, D, false >
	Static array allocation class that works for any type. More...

struct	StaticArrayTraits< T, D, true >
	Static array allocation class that is specialized for scalar i.e., fundamental or built-in types (float, double, etc...). More...

class	StaticFixedStorage
	Statically allocated storage class. More...

class	StaticStorage
	Statically allocated storage class. More...

class	GetMeanValsFunc
	Get mean values matrix for mean-based preconditioning. More...

class	GetMeanValsFunc< Kokkos::View< Sacado::UQ::PCE< Storage > *, P... > >
	Get mean values matrix for mean-based preconditioning. More...

class	GetMeanValsFunc< Kokkos::View< Sacado::MP::Vector< Storage > *, P... > >
	Get mean values matrix for mean-based preconditioning. More...

class	GetScalarMeanValsFunc
	Get mean values matrix for mean-based preconditioning. More...

class	GetScalarMeanValsFunc< Kokkos::View< Sacado::UQ::PCE< Storage > *, P... > >
	Get mean values matrix for mean-based preconditioning. More...

class	GetScalarMeanValsFunc< Kokkos::View< Sacado::MP::Vector< Storage > *, P... > >
	Get mean values matrix for mean-based preconditioning. More...

class	MeanBasedTpetraOperator

struct	error_storage_type_is_not_allocateable

struct	error_storage_type_is_not_resizeable

class	ViewStorage
	Dynamic storage with view semantics and contiguous access. More...

struct	is_ViewStorage

struct	is_ViewStorage< ViewStorage< ordinal_t, value_t, static_length, static_stride, device_t > >

class	Multiply< KokkosSparse::CrsMatrix< Sacado::MP::Vector< MatrixStorage >, MatrixOrdinal, MatrixDevice, MatrixMemory, MatrixSize >, Kokkos::View< Sacado::MP::Vector< InputStorage > , InputP... >, Kokkos::View< Sacado::MP::Vector< OutputStorage > , OutputP... > >

class	Multiply< KokkosSparse::CrsMatrix< Sacado::MP::Vector< MatrixStorage >, MatrixOrdinal, MatrixDevice, MatrixMemory, MatrixSize >, Kokkos::View< Sacado::MP::Vector< InputStorage > , InputP... >, Kokkos::View< Sacado::MP::Vector< OutputStorage > , OutputP... > >

struct	DeviceForNode
	Trait class that determines (new) Kokkos execution space type from Kokkos(Classic) Node type. More...

class	AlgebraicOrthogPolyExpansion
	Orthogonal polynomial expansions limited to algebraic operations. More...

class	AnisoSparseGridQuadrature
	Defines quadrature for a tensor product basis by anisotropic Smolyak sparse grids. More...

class	BasisFactory
	Factory for building multivariate orthogonal polynomial bases. More...

class	BlockPreconditioner

class	CGDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...

class	ClenshawCurtisLegendreBasis
	Legendre polynomial basis using Clenshaw-Curtis quadrature points. More...

class	CompletePolynomialBasis
	Multivariate orthogonal polynomial basis generated from a total-order complete-polynomial tensor product of univariate polynomials. More...

class	ConstantOrthogPolyExpansion
	Orthogonal polynomial expansion class for constant (size 1) expansions. More...

class	Dense3Tensor
	Data structure storing a dense 3-tensor C(i,j,k). More...

class	DenseDirectDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...

class	DerivBasis
	Abstract base class for multivariate orthogonal polynomials that support computing double and triple products involving derivatives of the basis polynomials. More...

class	DerivOrthogPolyExpansion
	Othogonal polynomial expansions based on derivative calculations. More...

class	DiagPreconditioner

class	DiscretizedStieltjesBasis
	Generates three-term recurrence using the Discretized Stieltjes procedure. More...

class	DivisionExpansionStrategy
	Strategy interface for computing PCE of a/b. More...

struct	IsScalarType
	Base template specification for IsScalarType. More...

struct	IsScalarType< float >

struct	IsScalarType< double >

struct	IsScalarType< int >

struct	IsScalarType< long >

struct	ds_array
	Dynamic array allocation class that works for any type. More...

struct	ds_array< T, true >
	Dynamic array allocation class that is specialized for scalar i.e., fundamental or built-in types (float, double, etc...). More...

class	ExpansionFactory
	Factory for building multivariate expansion strategies. More...

class	ForUQTKOrthogPolyExpansion

class	GaussPattersonLegendreBasis
	Legendre polynomial basis using Gauss-Patterson quadrature points. More...

class	GMRESDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...

class	GramSchmidtBasis
	Transforms a non-orthogonal multivariate basis to an orthogonal one using the Gram-Schmit procedure. More...

class	GrowthRule
	Interface for abstract growth rules. More...

class	IdentityGrowthRule
	A growth rule that is the identity. More...

class	LinearGrowthRule
	A linear growth rule. More...

class	EvenGrowthRule
	A growth rule that always makes the supplied order even. More...

class	ClenshawCurtisExponentialGrowthRule
	An exponential growth rule for Clenshaw-Curtis. More...

class	GaussPattersonExponentialGrowthRule
	An exponential growth rule for Gauss-Patterson. More...

class	GSPreconditioner

class	GSReducedPCEBasisBase
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	HermiteBasis
	Hermite polynomial basis. More...

class	InversePreconditioner

class	JacobiBasis
	Jacobi polynomial basis. More...

class	JacobiPreconditioner

class	WeightedVectorSpace

class	Lanczos
	Applies Lanczos procedure to a given matrix. More...

class	DiagonalOperator

class	LanczosPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...

class	DenseOperator

class	LanczosProjPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...

class	LegendreBasis
	Legendre polynomial basis. More...

class	LTBSparse3Tensor
	Data structure storing a sparse 3-tensor C(i,j,k) in a a tree-based format for lexicographically ordered product bases. More...

struct	LexicographicTreeBasisNode

struct	FlatLTBSparse3TensorNode

struct	FlatLTBSparse3Tensor

class	MeanBasedDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...

class	MonomialGramSchmidtPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	MonomialProjGramSchmidtPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	MonomialProjGramSchmidtPCEBasis2
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	OneDOrthogPolyBasis
	Abstract base class for 1-D orthogonal polynomials. More...

class	Operator

class	OrthogonalizationFactory
	Encapsulate various orthogonalization (ie QR) methods. More...

class	OrthogPolyApprox
	Class to store coefficients of a projection onto an orthogonal polynomial basis. More...

class	OrthogPolyBasis
	Abstract base class for multivariate orthogonal polynomials. More...

class	OrthogPolyExpansion
	Abstract base class for orthogonal polynomial-based expansions. More...

class	OrthogPolyExpansionBase
	Base class for consolidating common expansion implementations. More...

class	PecosOneDOrthogPolyBasis
	Implementation of OneDOrthogPolyBasis via Pecos. More...

class	ProductBasis
	Abstract base class for multivariate orthogonal polynomials generated from tensor products of univariate polynomials. More...

class	MultiIndex
	A multidimensional index. More...

class	TotalOrderIndexSet
	An isotropic total order index set. More...

class	AnisotropicTotalOrderIndexSet
	An anisotropic total order index set. More...

class	TensorProductIndexSet
	A tensor product index set. More...

class	TensorProductElement
	Container storing a term in a generalized tensor product. More...

class	LexographicLess
	A comparison functor implementing a strict weak ordering based lexographic ordering. More...

class	TotalOrderLess
	A comparison functor implementing a strict weak ordering based total-order ordering, recursive on the dimension. More...

class	MortonZLess
	A comparison functor implementing a strict weak ordering based Morton Z-ordering. More...

class	FloatingPointLess
	A functor for comparing floating-point numbers to some tolerance. More...

struct	TensorProductPredicate
	Predicate functor for building sparse triple products. More...

struct	TotalOrderPredicate
	Predicate functor for building sparse triple products based on total order. More...

class	ProductBasisUtils
	Utilities for indexing a multi-variate complete polynomial basis. More...

class	CompletePolynomialBasisUtils
	Utilities for indexing a multi-variate complete polynomial basis. More...

class	ProductLanczosGramSchmidtPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	ProductLanczosPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

struct	DefaultPointCompare
	Struct defining default point compare type. More...

class	PseudoSpectralOperator
	An operator interface for building pseudo-spectral approximations. More...

class	PseudoSpectralOperatorFactory
	Factory for building multivariate quadrature strategies. More...

class	PseudoSpectralOrthogPolyExpansion
	Orthogonal polynomial expansions based on numerical quadrature. More...

class	QuadOrthogPolyExpansion
	Orthogonal polynomial expansions based on numerical quadrature. More...

class	Quadrature
	Abstract base class for quadrature methods. More...

class	QuadratureFactory
	Factory for building multivariate quadrature strategies. More...

class	QuadraturePseudoSpectralOperator
	An operator for building pseudo-spectral coefficients using an arbitrary quadrature rule. More...

class	RecurrenceBasis
	Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship: $\gamma_{k+1}\psi_{k+1}(x) = (\delta_k x - \alpha_k)\psi_k(x) - \beta_k\psi_{k-1}(x)$ for $k=0,\dots,P$ where $\psi_{-1}(x) = 0$ , $\psi_{0}(x) = 1/\gamma_0$ , and $\beta_{0} = 1 = \int d\lambda$ . More...

class	ReducedBasisFactory
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	ReducedPCEBasis
	Abstract base class for reduced basis strategies built from polynomial chaos expansions in some other basis. More...

class	ReducedQuadratureFactory
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

class	RysBasis
	Rys polynomial basis. More...

class	SchurPreconditioner

class	SmolyakBasis
	Multivariate orthogonal polynomial basis generated from a Smolyak sparse grid. More...

class	SmolyakPseudoSpectralOperator
	An operator for building pseudo-spectral coefficients using a sparse Smolyak construction. More...

class	SmolyakSparseGridQuadrature
	Defines quadrature for a tensor product basis by Smolyak sparse grids. More...

class	Sparse3Tensor
	Data structure storing a sparse 3-tensor C(i,j,k) in a a compressed format. More...

class	RCB

struct	CijkData

class	SparseArrayIterator
	Bi-directional iterator for traversing a sparse array. More...

class	SparseArrayReverseIterator
	Bi-directional reverse iterator for traversing a sparse array. More...

struct	SparseArray
	Container for a "sparse" array. More...

class	SparseGridQuadrature
	Defines quadrature for a tensor product basis by Smolyak sparse grids. More...

class	SPDDenseDirectDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...

class	StandardStorage

class	StaticFixedStandardStorage
	Statically allocated storage class. More...

class	StaticStandardStorage
	Statically allocated storage class. More...

class	StieltjesBasis
	Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional mapping another basis. More...

class	StieltjesGramSchmidtBuilder
	Class for building a reduced-dimension basis and quadrature from a given set of polynomial chaos expansions. First generates 1-D orthogonal bases using the discretized Stieltjes procedure, forms their tensor product, and then orthogonalizes using Gram-Schmidt. More...

class	StieltjesPCEBasis
	Generates three-term recurrence using the Discretized Stieltjes procedure applied to a polynomial chaos expansion in another basis. More...

class	TensorProductBasis
	Multivariate orthogonal polynomial basis generated from a tensor product of univariate polynomials. More...

class	TensorProductPseudoSpectralOperator
	An operator for building pseudo-spectral coefficients using tensor-product quadrature. More...

class	TensorProductQuadrature
	Defines quadrature for a tensor product basis by tensor products of 1-D quadrature rules. More...

class	TotalOrderBasis
	Multivariate orthogonal polynomial basis generated from a total order tensor product of univariate polynomials. More...

class	UserDefinedQuadrature

Enumerations
enum	GrowthPolicy { SLOW_GROWTH, MODERATE_GROWTH }
	Enumerated type for determining Smolyak growth policies.

enum	CijkSymmetryType { CIJK_NO_SYMMETRY, CIJK_TWO_WAY_SYMMETRY, CIJK_SIX_WAY_SYMMETRY }

Functions
Teuchos::RCP< const EpetraExt::MultiComm >	buildMultiComm (const Epetra_Comm &globalComm, int num_global_stochastic_blocks, int num_spatial_procs=-1)

Teuchos::RCP< const Epetra_Comm >	getSpatialComm (const Teuchos::RCP< const EpetraExt::MultiComm > &globalMultiComm)

Teuchos::RCP< const Epetra_Comm >	getStochasticComm (const Teuchos::RCP< const EpetraExt::MultiComm > &globalMultiComm)

template<typename coeff_type >
std::ostream &	operator<< (std::ostream &os, const ProductContainer< coeff_type > &vec)

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Epetra_CrsGraph >	sparse3Tensor2CrsGraph (const Stokhos::OrthogPolyBasis< ordinal_type, value_type > &basis, const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_Comm &comm)
	Build an Epetra_CrsGraph from a sparse 3 tensor. More...

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Epetra_CrsGraph >	sparse3Tensor2CrsGraph (const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_BlockMap &map)
	Build an Epetra_CrsGraph from a sparse 3 tensor. More...

template<typename ordinal_type , typename value_type >
void	sparse3Tensor2MatrixMarket (const Stokhos::OrthogPolyBasis< ordinal_type, value_type > &basis, const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_Comm &comm, const std::string &file)

template<typename ordinal_type , typename value_type >
void	sparse3Tensor2MatrixMarket (const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_BlockMap &map, const std::string &file)

template<typename coeff_type >
std::ostream &	operator<< (std::ostream &os, const VectorOrthogPoly< coeff_type > &vec)

template<typename Scalar >
KOKKOS_INLINE_FUNCTION Scalar	shfl_down (const Scalar &val, const int &delta, const int &width)

template<typename Scalar >
KOKKOS_INLINE_FUNCTION Scalar	shfl_up (const Scalar &val, const int &delta, const int &width)

template<typename Scalar >
KOKKOS_INLINE_FUNCTION Scalar	shfl_down (const Scalar &val, const int &delta, const int &width, const int &mask)

template<typename Scalar >
KOKKOS_INLINE_FUNCTION Scalar	shfl_up (const Scalar &val, const int &delta, const int &width, const int &mask)

KOKKOS_INLINE_FUNCTION void	sync_warp (const int &mask)

template<class Device , bool Pack, typename OrdinalType , typename ValueType >
CooProductTensor< ValueType, Device, Pack >	create_coo_product_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<typename ValueType , typename Device , bool Pack>
std::ostream &	operator<< (std::ostream &os, const CooProductTensor< ValueType, Device, Pack > &tensor)

template<typename MatrixValue , typename Layout , typename Device , typename InputMultiVectorType , typename OutputMultiVectorType , typename OrdinalType >
void	multiply (const CrsMatrix< MatrixValue, Device, Layout > &A, const InputMultiVectorType &x, OutputMultiVectorType &y, const std::vector< OrdinalType > &col_indices, SingleColumnMultivectorMultiply)

template<typename MatrixValue , typename Layout , typename Device , typename InputVectorType , typename OutputVectorType >
void	multiply (const CrsMatrix< MatrixValue, Device, Layout > &A, const std::vector< InputVectorType > &x, std::vector< OutputVectorType > &y, SingleColumnMultivectorMultiply)

template<class Device , typename OrdinalType , typename ValueType >
CrsProductTensor< ValueType, Device >	create_product_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<class Device , typename OrdinalType , typename ValueType , class Memory >
CrsProductTensor< ValueType, Device, Memory >	create_product_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<class Device , typename OrdinalType , typename ValueType >
CrsProductTensor< ValueType, Device >	create_mean_based_product_tensor ()

template<class Device , typename OrdinalType , typename ValueType , class Memory >
CrsProductTensor< ValueType, Device, Memory >	create_mean_based_product_tensor ()

template<class ValueType , class Device , class Memory >
CrsProductTensor< ValueType, Device, Memory >::HostMirror	create_mirror_view (const CrsProductTensor< ValueType, Device, Memory > &src)

template<class ValueType , class DstDevice , class DstMemory , class SrcDevice , class SrcMemory >
void	deep_copy (const CrsProductTensor< ValueType, DstDevice, DstMemory > &dst, const CrsProductTensor< ValueType, SrcDevice, SrcMemory > &src)

template<class Device , typename OrdinalType , typename ValueType >
FlatSparse3Tensor< ValueType, Device >	create_flat_sparse_3_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<class Device , typename OrdinalType , typename ValueType >
FlatSparse3Tensor_kji < ValueType, Device >	create_flat_sparse_3_tensor_kji (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<class Device , typename OrdinalType , typename ValueType >
LexicographicBlockSparse3Tensor < ValueType, Device >	create_lexicographic_block_sparse_3_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::LTBSparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<class Device , typename OrdinalType , typename ValueType , int BlockSize>
LinearSparse3Tensor< ValueType, Device, BlockSize >	create_linear_sparse_3_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params)

template<typename MatrixType >
void	write_matrix_market (const MatrixType &A, const std::string &filename)

template<typename MatrixType , typename InputVectorType , typename OutputVectorType >
void	multiply (const MatrixType &A, const InputVectorType &x, OutputVectorType &y)

template<typename MatrixType , typename InputVectorType , typename OutputVectorType >
void	multiply (const MatrixType &A, const InputVectorType &x, OutputVectorType &y, DefaultMultiply tag)

template<typename MatrixType , typename InputVectorType , typename OutputVectorType , typename ColumnIndicesType >
void	multiply (const MatrixType &A, const InputVectorType &x, OutputVectorType &y, const ColumnIndicesType &col)

template<typename MatrixType , typename InputVectorType , typename OutputVectorType , typename ColumnIndicesType >
void	multiply (const MatrixType &A, const InputVectorType &x, OutputVectorType &y, const ColumnIndicesType &col, DefaultMultiply tag)

template<class Device , typename OrdinalType , typename ValueType >
SimpleTiledCrsProductTensor < ValueType, Device >	create_simple_tiled_product_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params)

template<typename TensorType , typename OrdinalType , typename ValueType , typename CijkType >
StochasticProductTensor < ValueType, TensorType, typename TensorType::execution_space >	create_stochastic_product_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const CijkType &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())

template<class Device , typename OrdinalType , typename ValueType >
TiledCrsProductTensor < ValueType, Device >	create_tiled_product_tensor (const Stokhos::ProductBasis< OrdinalType, ValueType > &basis, const Stokhos::Sparse3Tensor< OrdinalType, ValueType > &Cijk, const Teuchos::ParameterList &params)

template<typename ValueType , typename VectorType >
void	update (const ValueType &alpha, VectorType &x, const ValueType &beta, const VectorType &y)

template<typename T , typename U >
bool	operator== (const aligned_allocator< T > &, const aligned_allocator< U > &)

template<typename T , typename U >
bool	operator!= (const aligned_allocator< T > &, const aligned_allocator< U > &)

template<typename Scalar , typename LO , typename GO , typename N >
Teuchos::RCP < Tpetra::CrsMatrix< Scalar, LO, GO, N > >	build_mean_matrix (const Tpetra::CrsMatrix< Scalar, LO, GO, N > &A)

template<typename Scalar , typename LO , typename GO , typename N >
Teuchos::RCP < Tpetra::CrsMatrix< typename Scalar::value_type, LO, GO, N > >	build_mean_scalar_matrix (const Tpetra::CrsMatrix< Scalar, LO, GO, N > &A)

template<typename DstView , typename SrcView >
void	copy_pce_to_scalar (const DstView &dst, const SrcView &src)

template<typename DstView , typename SrcView >
void	copy_scalar_to_pce (const DstView &dst, const SrcView &src)

template<typename Matrix , typename Vector , typename Ordinal >
bool	CG_Solve (const Matrix &A, Vector &x, const Vector &b, typename Vector::mag_type tol, Ordinal max_its, std::ostream *out=0)

template<typename Matrix , typename Vector , typename Prec , typename Ordinal >
bool	PCG_Solve (const Matrix &A, Vector &x, const Vector &b, const Prec &M, typename Vector::mag_type tol, Ordinal max_its, std::ostream *out=0)

template<typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< Tpetra::Map < LocalOrdinal, GlobalOrdinal, Node > >	create_flat_map (const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > &map, const LocalOrdinal block_size)

template<typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< Tpetra::CrsGraph < LocalOrdinal, GlobalOrdinal, Node > >	create_flat_mp_graph (const Tpetra::CrsGraph< LocalOrdinal, GlobalOrdinal, Node > &graph, Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_domain_map, Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_range_map, const LocalOrdinal block_size)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< const Tpetra::MultiVector< typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (const Tpetra::MultiVector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec_const, const Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< const Tpetra::MultiVector< typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (const Tpetra::MultiVector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec, Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP < Tpetra::MultiVector < typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (Tpetra::MultiVector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec, const Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP < Tpetra::MultiVector < typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (Tpetra::MultiVector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec, Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< const Tpetra::Vector< typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (const Tpetra::Vector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec_const, const Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< const Tpetra::Vector< typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (const Tpetra::Vector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec, Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< Tpetra::Vector < typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (Tpetra::Vector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec, const Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP< Tpetra::Vector < typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_vector_view (Tpetra::Vector< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &vec, Teuchos::RCP< const Tpetra::Map< LocalOrdinal, GlobalOrdinal, Node > > &flat_map)

template<typename Storage , typename LocalOrdinal , typename GlobalOrdinal , typename Node >
Teuchos::RCP < Tpetra::CrsMatrix< typename Storage::value_type, LocalOrdinal, GlobalOrdinal, Node > >	create_flat_matrix (const Tpetra::CrsMatrix< Sacado::MP::Vector< Storage >, LocalOrdinal, GlobalOrdinal, Node > &mat, const Teuchos::RCP< const Tpetra::CrsGraph< LocalOrdinal, GlobalOrdinal, Node > > &flat_graph, const LocalOrdinal block_size)

template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const Dense3Tensor< ordinal_type, value_type > &Cijk)

template<typename ordinal_type >
Teuchos::RCP < LexicographicTreeBasisNode < ordinal_type > >	build_lexicographic_basis_tree (const Teuchos::ArrayView< const ordinal_type > &basis_orders, const ordinal_type total_order, const ordinal_type index_begin=ordinal_type(0), const ordinal_type order_sum=ordinal_type(0), const Stokhos::MultiIndex< ordinal_type > &term_prefix=Stokhos::MultiIndex< ordinal_type >())

template<typename ordinal_type , typename value_type >
Teuchos::RCP< LTBSparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensorLTB (const TotalOrderBasis< ordinal_type, value_type, LexographicLess< MultiIndex< ordinal_type > > > &product_basis, bool symmetric=false)

template<typename ordinal_type , typename value_type >
Teuchos::RCP< typename LTBSparse3Tensor< ordinal_type, value_type >::CijkNode >	computeCijkLTBNode (const Teuchos::ArrayView< const ordinal_type > &basis_orders, const Teuchos::ArrayView< const Teuchos::RCP< Sparse3Tensor< ordinal_type, value_type > > > &Cijk_1d, const Teuchos::RCP< LexicographicTreeBasisNode< ordinal_type > > &i_ltb, const Teuchos::RCP< LexicographicTreeBasisNode< ordinal_type > > &j_ltb, const Teuchos::RCP< LexicographicTreeBasisNode< ordinal_type > > &k_ltb, const ordinal_type total_order, const bool symmetric, const ordinal_type sum_i=ordinal_type(0), const ordinal_type sum_j=ordinal_type(0), const ordinal_type sum_k=ordinal_type(0), const value_type cijk_base=value_type(1))

template<typename ordinal_type , typename value_type >
Teuchos::RCP< LTBSparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensorLTBBlockLeaf (const TotalOrderBasis< ordinal_type, value_type, LexographicLess< MultiIndex< ordinal_type > > > &product_basis, bool symmetric=false)

template<typename ordinal_type , typename value_type >
Teuchos::RCP< typename LTBSparse3Tensor< ordinal_type, value_type >::CijkNode >	computeCijkLTBNodeBlockLeaf (const Teuchos::ArrayView< const ordinal_type > &basis_orders, const Teuchos::ArrayView< const Teuchos::RCP< Dense3Tensor< ordinal_type, value_type > > > &Cijk_1d, const Teuchos::RCP< LexicographicTreeBasisNode< ordinal_type > > &i_ltb, const Teuchos::RCP< LexicographicTreeBasisNode< ordinal_type > > &j_ltb, const Teuchos::RCP< LexicographicTreeBasisNode< ordinal_type > > &k_ltb, const ordinal_type total_order, const bool symmetric, const ordinal_type sum_i=ordinal_type(0), const ordinal_type sum_j=ordinal_type(0), const ordinal_type sum_k=ordinal_type(0), const value_type cijk_base=value_type(1), const bool parent_j_equals_k=true)

template<typename ordinal_type , typename value_type >
Teuchos::RCP < FlatLTBSparse3Tensor < ordinal_type, value_type > >	computeFlatTripleProductTensorLTB (const TotalOrderBasis< ordinal_type, value_type, LexographicLess< MultiIndex< ordinal_type > > > &product_basis, bool symmetric=false)

template<int max_size, typename ordinal_type , typename value_type >
void	flatLTB3TensorMultiply (OrthogPolyApprox< ordinal_type, value_type > &c, const OrthogPolyApprox< ordinal_type, value_type > &a, const OrthogPolyApprox< ordinal_type, value_type > &b, const FlatLTBSparse3Tensor< ordinal_type, value_type > &cijk)

template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const OneDOrthogPolyBasis< ordinal_type, value_type > &b)
	Print basis to stream `os`.

template<typename ordinal_type , typename value_type , typename node_type >
std::ostream &	operator<< (std::ostream &os, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)
	Prints the array of coefficients (more compact than print())

template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const OrthogPolyBasis< ordinal_type, value_type > &b)
	Print basis to stream `os`.

template<typename ordinal_type >
ordinal_type	n_choose_k (const ordinal_type &n, const ordinal_type &k)
	Compute bionomial coefficient (n ; k) = n!/( k! (n-k)! )

template<typename ordinal_type >
std::ostream &	operator<< (std::ostream &os, const MultiIndex< ordinal_type > &m)

template<typename ordinal_type , typename element_type >
std::ostream &	operator<< (std::ostream &os, const TensorProductElement< ordinal_type, element_type > &m)

template<typename ordinal_type >
ordinal_type	totalOrderMapping (const Stokhos::MultiIndex< ordinal_type > &index)

template<typename ordinal_type >
ordinal_type	lexicographicMapping (const Stokhos::MultiIndex< ordinal_type > &index, ordinal_type max_order)

template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const Quadrature< ordinal_type, value_type > &quad)
	Print quadrature object to stream.

template<typename ordinal_type , typename scalar_type >
void	print_matlab (std::ostream &os, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A)

template<typename ordinal_type , typename scalar_type >
scalar_type	vec_norm_inf (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A)
	Vector-infinity norm of a matrix.

template<typename ordinal_type , typename scalar_type >
void	QR_CGS (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using classical Gram-Schmidt. More...

template<typename ordinal_type , typename scalar_type >
void	QR_MGS (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using modified Gram-Schmidt. More...

template<typename ordinal_type , typename scalar_type >
void	QR_MGS2 (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using modified Gram-Schmidt with reorthogonalization. More...

template<typename ordinal_type , typename scalar_type >
void	QR_Householder (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using Householder reflections. More...

template<typename ordinal_type , typename scalar_type >
void	CPQR_Householder3 (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using Householder reflections. More...

template<typename ordinal_type , typename scalar_type >
ordinal_type	CPQR_Householder_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using Householder reflections. More...

template<typename ordinal_type , typename scalar_type >
ordinal_type	CPQR_MGS_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using modified Gram-Schmidt. More...

template<typename ordinal_type , typename scalar_type >
ordinal_type	CPQR_MGS_reorthog_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using modified Gram-Schmidt and reorthogonalization. More...

template<typename ordinal_type , typename scalar_type >
scalar_type	cond_R (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute condition number of upper-triangular R.

template<typename ordinal_type , typename scalar_type >
scalar_type	weightedQROrthogonalizationError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::Array< scalar_type > &w)
	Compute weighted QR orthogonalization error. More...

template<typename ordinal_type , typename scalar_type >
scalar_type	QROrthogonalizationError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q)
	Compute QR orthogonalization error. More...

template<typename ordinal_type , typename scalar_type >
scalar_type	residualQRError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute QR residual error. More...

template<typename ordinal_type , typename scalar_type >
scalar_type	residualCPQRError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, const Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR residual error. More...

template<typename ordinal_type , typename scalar_type >
void	svd (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::Array< scalar_type > &s, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &U, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Vt)
	Compute SVD of matrix. More...

template<typename ordinal_type , typename scalar_type >
ordinal_type	svd_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::Array< scalar_type > &s, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &U, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Vt)

template<typename ordinal_type , typename scalar_type >
Teuchos::ArrayRCP< CijkData < ordinal_type, scalar_type > >	build_cijk_coordinate_list (const Sparse3Tensor< ordinal_type, scalar_type > &Cijk, CijkSymmetryType symmetry_type)

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Sparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensorLTO (const TotalOrderBasis< ordinal_type, value_type, LexographicLess< MultiIndex< ordinal_type > > > &product_basis, bool symmetric=false)

Detailed Description

Top-level namespace for Stokhos classes and functions.

Function Documentation

template<typename ordinal_type , typename scalar_type >

void Stokhos::CPQR_Householder3	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using Householder reflections.

For A an m-by-n matrix with m >= n, computes A*P = Q*R with R n-by-n upper triangular and Q m-by-n with orthogonal columns (often called the economy size QR) and P an m-by-n permutation matrix. For n >= m, computes A*P = Q*R with R m-by-n upper trapezoidal and Q m-by-m upper trapezoidal (R = [R_1 R_2] with R_1 upper triangular and R_2 rectangular). For k = min(m,n), both cases are handled with Q m-by-k and R k-by-n.

The QR factorization is computed by the corresponding LAPACK function. This version uses the BLAS3-rich xGEQP3.

Referenced by CPQR_Householder_threshold().

template<typename ordinal_type , typename scalar_type >

ordinal_type Stokhos::CPQR_Householder_threshold	(	const scalar_type &	rank_threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using Householder reflections.

For A an m-by-n matrix, computes A*P = Q*R with R k-by-k upper triangular, Q m-by-k with orthonormal columns, and P an n-by-k permutation matrix. Here k <= min(m,n) is determined by a rank threshold tau provided by the user. The resulting R will have cond(R) <= 1/tau. P is returned in the pivot array piv and the rank k returned by the function. Only the first k entries of piv will be set. As with LAPACK, the user can require columns of A to be included in P by setting the corresponding entries of piv to be nonzero on input.

If make_R_square is false then R is k-by-n.

This ultimately uses the LAPACK column-pivoted QR function which does a full QR factorization. This then extracts the parts of Q, R, and P determined by the threshold as described above. As such, this function requires the weight vector to be 1 (Note the weight vector will be ignored if it is size 0).

References CPQR_Householder3().

Referenced by Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

ordinal_type Stokhos::CPQR_MGS_reorthog_threshold	(	const scalar_type &	rank_threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using modified Gram-Schmidt and reorthogonalization.

For A an m-by-n matrix, computes A*P = Q*R with R k-by-k upper triangular, Q m-by-k with orthonormal columns, and P an n-by-k permutation matrix. Here k <= min(m,n) is determined by a rank threshold tau provided by the user. The resulting R will have cond(R) <= 1/tau. P is returned in the pivot array piv and the rank k returned by the function. Only the first k entries of piv will be set. As with LAPACK, the user can require columns of A to be included in P by setting the corresponding entries of piv to be nonzero on input. The orthogonality of Q is determined by the weight vector w, defining a weighted inner-product.

References CPQR_MGS_threshold(), and QR_MGS().

Referenced by Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

ordinal_type Stokhos::CPQR_MGS_threshold	(	const scalar_type &	rank_threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using modified Gram-Schmidt.

For A an m-by-n matrix, computes A*P = Q*R with R k-by-k upper triangular, Q m-by-k with orthonormal columns, and P an n-by-k permutation matrix. Here k <= min(m,n) is determined by a rank threshold tau provided by the user. The resulting R will have cond(R) <= 1/tau. P is returned in the pivot array piv and the rank k returned by the function. Only the first k entries of piv will be set. As with LAPACK, the user can require columns of A to be included in P by setting the corresponding entries of piv to be nonzero on input. The orthogonality of Q is determined by the weight vector w, defining a weighted inner-product.

Referenced by CPQR_MGS_reorthog_threshold(), and Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_CGS	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using classical Gram-Schmidt.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_Householder	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using Householder reflections.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

The QR factorization is computed by the corresponding LAPACK function.

Referenced by Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_MGS	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using modified Gram-Schmidt.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

Referenced by CPQR_MGS_reorthog_threshold(), and Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_MGS2	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using modified Gram-Schmidt with reorthogonalization.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

Referenced by Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::QROrthogonalizationError ( const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > & Q )

Compute QR orthogonalization error.

Computes ||Q^T*Q-I||_infinity for Q coming from a QR factorization.

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::residualCPQRError	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		const Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR residual error.

Computes ||Q*R-A*P||_infinity for Q,R coming from a column-pivoted QR factorization.

Works with thin or full QR, weighted or not.

Referenced by Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::residualQRError	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute QR residual error.

Computes ||Q*R-A||_infinity for Q,R coming from QR factorization.

Works with thin or full QR, weighted or not.

template<typename ordinal_type , typename value_type >

Teuchos::RCP<Epetra_CrsGraph> Stokhos::sparse3Tensor2CrsGraph	(	const Stokhos::OrthogPolyBasis< ordinal_type, value_type > &	basis,
		const Stokhos::Sparse3Tensor< ordinal_type, value_type > &	Cijk,
		const Epetra_Comm &	comm
	)

Build an Epetra_CrsGraph from a sparse 3 tensor.

Builds a sparse graph from a sparse 3 tensor by summing over the third index. This graph then represents the sparsity pattern of the stochastic part of the block stochastic Galerkin operator. Redistributing the graph should then provide a suitable parallel distribution for block stochastic Galerkin linear solves.

References Stokhos::Sparse3Tensor< ordinal_type, value_type >::i_begin(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::i_end(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::j_begin(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::j_end(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::k_begin(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::k_end(), and Stokhos::OrthogPolyBasis< ordinal_type, value_type >::size().

Referenced by Stokhos::EpetraSparse3Tensor::EpetraSparse3Tensor().

template<typename ordinal_type , typename value_type >

Teuchos::RCP<Epetra_CrsGraph> Stokhos::sparse3Tensor2CrsGraph	(	const Stokhos::Sparse3Tensor< ordinal_type, value_type > &	Cijk,
		const Epetra_BlockMap &	map
	)

Build an Epetra_CrsGraph from a sparse 3 tensor.

Builds a sparse graph from a sparse 3 tensor by summing over the third index. This graph then represents the sparsity pattern of the stochastic part of the block stochastic Galerkin operator. Redistributing the graph should then provide a suitable parallel distribution for block stochastic Galerkin linear solves.

References Stokhos::Sparse3Tensor< ordinal_type, value_type >::i_begin(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::i_end(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::j_begin(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::j_end(), Stokhos::Sparse3Tensor< ordinal_type, value_type >::k_begin(), and Stokhos::Sparse3Tensor< ordinal_type, value_type >::k_end().

template<typename ordinal_type , typename scalar_type >

void Stokhos::svd	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		Teuchos::Array< scalar_type > &	s,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	U,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Vt
	)

Compute SVD of matrix.

The SVD is computed by the corresponding LAPACK function.

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::weightedQROrthogonalizationError	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		const Teuchos::Array< scalar_type > &	w
	)

Compute weighted QR orthogonalization error.

Computes ||Q^T*W*Q-I||_infinity for Q coming from a weighted QR factorization.

Referenced by Stokhos::OrthogonalizationFactory< ordinal_type, value_type >::createOrthogonalBasis().

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